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Almost automorphic solutions of certain abstract differential equations. (English) Zbl 0304.42028

42A75Classical almost periodic functions, mean periodic functions
34C25Periodic solutions of ODE
Full Text: DOI
[1] S. Bochner,Uniform convergence of monotone sequences of functions, Proc. Nat. Acad. Sci. U.S.,47 (1961), pp. 582--585. · Zbl 0103.05304 · doi:10.1073/pnas.47.4.582
[2] S. Bochner,Continuous mappings of almost automorphic and almost periodic functions, Proc. Nat. Acad. Sc. U.S.,52 (1964), pp. 907--910. · Zbl 0134.30102 · doi:10.1073/pnas.52.4.907
[3] C. Corduneanu,Almost periodic functions, Interscience Tract in Mathematics Number 22, John Wiley and Sons, New York, U.S.A. · Zbl 1240.42115
[4] M. M. Day,Normed linear spaces, Springer-Verlag, Berlin, 1962. · Zbl 0100.10802
[5] H. Günzler -S. Zaidman,Almost periodic solutions of a certain abstract differential equation. Journal of Mathematics and Mechanics,19, no. 2 (August 1969), pp. 155--158. · Zbl 0184.18104
[6] E. Hille - R. S. Phillips,Functional Analysis and Semigroups, Am. Math. Soc. Coll., Publications XXXI (1968 printing).
[7] W. A. Veech,Almost automorphic functions on groups, American Journal of Mathematics,87, no. 3 (July 1965), pp. 719--751. · Zbl 0137.05803 · doi:10.2307/2373071
[8] K. Yosida,Functional Analysis, Second edition Springer-Verlag, New York, 1968. · Zbl 0152.32102
[9] S. Zaidman,An existence theorem for bounded vector valued functions, Annali della Scuola Normale Superiore di Pisa, Classe di Scienze,24, fasc. 1 (1970). · Zbl 0206.44401
[10] S. Zaidman,On some almost periodic functions, Annali dell’Università di Ferrara (Nuova Serie), Sezione VII, Scienze Matematiche,19, no. 5.
[11] S. Zaidman,Weak almost periodicity for some vector valued functions, Istituto Lombardo (Rend. Sc.) A, 1970. · Zbl 0222.43007
[12] S. Zaidman,Some asymptotic theorems for abstract differential equations, Proc. Amer. Math. Soc.,25 (July 1970). · Zbl 0206.38505
[13] S. Zaidman,Sur la perturbation presque-periodique des groupes et semi-groupes de transformations d’un espace de Banach, Rend. Matem. e sue appl., Serie V,16 (1957), pp. 197--206. · Zbl 0089.32703
[14] L. Amerio,Sull’integrazione delle funzioni quasi-periodiche astratte, Ann. di Mat.,53 (1961). · Zbl 0099.10701